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MIT OpenCourseWareMIT 18.06 Linear Algebra, Spring 2005 (1999)

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This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.


This movie is part of the collection: MIT OpenCourseWare

Producer: MIT OpenCourseWare
Production Company: MIT OpenCourseWare
Audio/Visual: sound, color
Language: English - US
Keywords: systems of equations, vector spaces, positive definite matrices, matrix theory, linear algebra, determinants, eigenvalues, similarity, least-squares approximations, stability of differential equations, networks, Fourier transforms, Markov processes

Creative Commons license: Attribution-Noncommercial-Share Alike 3.0 United States


Individual Files

Movie Files h.264 Ogg Video Real Media
The Geometry of Linear Equations 237.2 MB 
161.1 MB 
56.7 MB 
Elimination with Matrices 295.2 MB 
193.8 MB 
70.6 MB 
Multiplication and Inverse Matrices 292.7 MB 
191.0 MB 
69.8 MB 
Factorization into A = LU 297.3 MB 
200.1 MB 
71.6 MB 
Transposes, Permutations, Spaces R^n 280.8 MB 
194.7 MB 
70.5 MB 
Column Space and Nullspace 270.9 MB 
190.0 MB 
67.9 MB 
Solving Ax = 0: Pivot Variables, Special Solutions 257.7 MB 
176.3 MB 
61.6 MB 
Solving Ax = b: Row Reduced Form R 281.0 MB 
192.1 MB 
66.5 MB 
Independence, Basis, and Dimension 297.8 MB 
201.0 MB 
71.4 MB 
The Four Fundamental Subspaces 290.2 MB 
198.0 MB 
73.1 MB 
Matrix Spaces; Rank 1; Small World Graphs 271.8 MB 
188.6 MB 
68.0 MB 
Graphs, Networks, Incidence Matrices 285.3 MB 
195.1 MB 
68.2 MB 
Quiz 1 Review 283.6 MB 
188.8 MB 
67.2 MB 
Orthogonal Vectors and Subspaces 295.9 MB 
202.6 MB 
70.9 MB 
Projections onto Subspaces 290.5 MB 
193.5 MB 
69.0 MB 
Projection Matrices and Least Squares 285.9 MB 
193.2 MB 
67.8 MB 
Orthogonal Matrices and Gram-Schmidt 293.9 MB 
200.3 MB 
69.6 MB 
Properties of Determinants 292.9 MB 
198.6 MB 
70.0 MB 
Determinant Formulas and Cofactors 317.3 MB 
217.3 MB 
76.1 MB 
Cramer's Rule, Inverse Matrix, and Volume 303.7 MB 
208.1 MB 
72.5 MB 
Eigenvalues and Eigenvectors 305.3 MB 
203.2 MB 
73.3 MB 
Diagonalization and Powers of A 308.5 MB 
209.4 MB 
73.9 MB 
Differential Equations and exp(At) 304.0 MB 
206.8 MB 
72.8 MB 
Markov Matrices; Fourier Series 305.0 MB 
208.6 MB 
73.0 MB 
Quiz 2 Review 287.7 MB 
195.7 MB 
69.0 MB 
Symmetric Matrices and Positive Definiteness 261.3 MB 
176.9 MB 
62.5 MB 
Complex Matrices; Fast Fourier Transform 284.4 MB 
187.5 MB 
68.1 MB 
Positive Definite Matrices and Minima 301.2 MB 
203.9 MB 
72.1 MB 
Similar Matrices and Jordan Form 273.4 MB 
183.4 MB 
65.5 MB 
Singular Value Decomposition 241.0 MB 
161.3 MB 
57.8 MB 
Linear Transformations and Their Matrices 294.1 MB 
199.5 MB 
70.4 MB 
Change of Basis; Image Compression 299.0 MB 
205.6 MB 
71.5 MB 
Quiz 3 Review 280.0 MB 
191.0 MB 
66.9 MB 
Left and Right Inverses; Pseudoinverse 248.8 MB 
169.5 MB 
59.5 MB 
Final Course Review 258.2 MB 
173.6 MB 
61.8 MB 
Image Files Thumbnail Animated GIF
The Geometry of Linear Equations 7.1 KB 
446.2 KB 
Elimination with Matrices 7.5 KB 
433.0 KB 
Multiplication and Inverse Matrices 6.5 KB 
426.5 KB 
Factorization into A = LU 5.8 KB 
442.3 KB 
Transposes, Permutations, Spaces R^n 6.2 KB 
448.8 KB 
Column Space and Nullspace 6.8 KB 
461.5 KB 
Solving Ax = 0: Pivot Variables, Special Solutions 5.3 KB 
440.2 KB 
Solving Ax = b: Row Reduced Form R 5.6 KB 
451.0 KB 
Independence, Basis, and Dimension 6.9 KB 
449.9 KB 
The Four Fundamental Subspaces 5.8 KB 
453.8 KB 
Matrix Spaces; Rank 1; Small World Graphs 6.2 KB 
443.7 KB 
Graphs, Networks, Incidence Matrices 5.8 KB 
448.4 KB 
Quiz 1 Review 5.9 KB 
429.7 KB 
Orthogonal Vectors and Subspaces 8.4 KB 
452.1 KB 
Projections onto Subspaces 7.3 KB 
437.0 KB 
Projection Matrices and Least Squares 7.0 KB 
455.4 KB 
Orthogonal Matrices and Gram-Schmidt 6.6 KB 
452.9 KB 
Properties of Determinants 6.7 KB 
443.0 KB 
Determinant Formulas and Cofactors 8.0 KB 
469.5 KB 
Cramer's Rule, Inverse Matrix, and Volume 7.8 KB 
461.8 KB 
Eigenvalues and Eigenvectors 7.4 KB 
448.9 KB 
Diagonalization and Powers of A 7.0 KB 
464.7 KB 
Differential Equations and exp(At) 6.4 KB 
453.1 KB 
Markov Matrices; Fourier Series 5.1 KB 
444.4 KB 
Quiz 2 Review 5.2 KB 
447.7 KB 
Symmetric Matrices and Positive Definiteness 6.5 KB 
446.5 KB 
Complex Matrices; Fast Fourier Transform 6.3 KB 
439.5 KB 
Positive Definite Matrices and Minima 7.2 KB 
458.5 KB 
Similar Matrices and Jordan Form 6.3 KB 
461.6 KB 
Singular Value Decomposition 8.0 KB 
467.8 KB 
Linear Transformations and Their Matrices 7.1 KB 
452.3 KB 
Change of Basis; Image Compression 7.8 KB 
445.7 KB 
Quiz 3 Review 7.1 KB 
450.1 KB 
Left and Right Inverses; Pseudoinverse 7.9 KB 
458.8 KB 
Final Course Review 7.2 KB 
441.0 KB 
Information FormatSize
MIT18.06S05_files.xml Metadata [file] 
MIT18.06S05_meta.xml Metadata 1.2 KB 
MIT18.06S05_reviews.xml Metadata 1.1 KB 

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Average Rating: 5.00 out of 5 stars5.00 out of 5 stars5.00 out of 5 stars5.00 out of 5 stars5.00 out of 5 stars

Reviewer: cjfsyntropy - 5.00 out of 5 stars5.00 out of 5 stars5.00 out of 5 stars5.00 out of 5 stars5.00 out of 5 stars - April 24, 2011
Subject: Study Linear algebra with Gilbert Strang
Glibert Strang’s 18.06 Linear Algebra course at MIT OpenCourseWare is exquisite!

Some of the course highlights are:
- Matrix focus (that is, more concrete and less abstract)
- An interesting take on “the fundamental theorem of linear algebra”
- A thorough treatment of projection matrices including applications to least squares (Strang revisits them over and over again)
- The idea of fundamental matrix factorizations as actions that “record” the essence of the algorithms of linear algebra

And more. I wrote a full review at http://blog.cjfearnley.com/2011/04/15/study-linear-algebra-at-mit-with-gilbert-strang/